Point Slope form definition
The point slope form definition provides an effective way to equation of straight line given a single point and slope. The method involves plotting the point and slope on a graph to get the equation for straight line. The name Point-Slope Form comes because it involves a single point and the slope of line to derive the equation.
Point Slope form equation for straight line:
The point slope form equation is derived for 2 dimensions i.e. x an y axis. A graph can also be plotted on a 2D axis with a point and the slope to it. It explains that the difference in y co-ordinates of any 2 given points on a line is directly proportional to the difference of x co-ordinates.
Point Slope form formula for straight line:
Given a point (x1,y1) and slope m, the point slope form formula is y-y1 = m(x-x1). This formula proves the proportionality between y co-ordinates and the x ones. The figure given below shows a straight line passing through 2 points and having slope m, being plotted on a 2D graph.
Now let's find the equation of a line passing through point (6,5) and having slope of 3. From the point slope form equation, we can write (y-5) = 3(x-6). Solving further gives 3x – y -13 =0 which is the equation of a straight line passing through (6,5) with slope 3. Thus we have got the idea of finding equation of a straight line using a single point and slope. The slope can be founded out easily by extending the lines from two points and than taking the ratio of difference of y co-ordinates to that of x co-ordinates. Thus point-slope form makes it easier finding the equation of a line.
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